To summarise, for \(K\) -WA the largest \(K\) -weighted bisimulation \(\sim _w\)  is strictly
included in \(K\) -weighted language equivalence \(\sim _l\)  as shown in
Proposition REF . Corollary REF  shows that
for \(K\) -LWA \(K\) -linear language equivalence
coincides with the largest \(K\) -linear bisimulation. This raises the question:
what is the relationship between \(K\) -weighted bisimulation and \(K\) -linear
bisimulation? Again, our answer extends that of [1]} to
the semimodule setting.
